# Synchronization in complex oscillator networks and smart grids

@article{Drfler2013SynchronizationIC, title={Synchronization in complex oscillator networks and smart grids}, author={Florian D{\"o}rfler and Michael Chertkov and Francesco Bullo}, journal={Proceedings of the National Academy of Sciences}, year={2013}, volume={110}, pages={2005 - 2010} }

The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. [...] Key Method Our synchronization condition can be stated elegantly in terms of the network topology and parameters or equivalently in terms of an intuitive, linear, and static auxiliary system. Our results significantly improve upon the existing conditions advocated thus far, they are provably exact for various interesting network topologies and parameters; they are statistically… Expand

## 673 Citations

Exploring synchronization in complex oscillator networks

- Physics, Computer Science2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
- 2012

A tutorial introduction to coupled oscillator networks, a review of the vast literature on theory and applications, and a collection of different synchronization notions, conditions, and analysis approaches are presented.

Control of coupled oscillator networks with application to microgrid technologies

- Computer Science, PhysicsScience Advances
- 2015

This work develops a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized state.

Synchronization assessment in power networks and coupled oscillators

- Mathematics, Computer Science2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
- 2012

A novel synchronization condition applicable to a general coupled oscillator model is presented and it is rigorously established that the condition is exact for various interesting network topologies and parameters.

When is sync globally stable in sparse networks of identical Kuramoto oscillators?

- Computer Science, PhysicsPhysica A: Statistical Mechanics and its Applications
- 2019

Optimal synchronization of directed complex networks.

- Computer Science, MedicineChaos
- 2016

Using the generalized synchrony alignment function, it is shown that a network's synchronization properties can be systematically optimized and promoted by a strong alignment of the natural frequencies with the left singular vectors corresponding to the largest singular values of the Laplacian matrix.

Stability Conditions for Cluster Synchronization in Networks of Heterogeneous Kuramoto Oscillators

- Computer Science, PhysicsIEEE Transactions on Control of Network Systems
- 2020

Quantitative conditions on the network weights, cluster configuration, and oscillators’ natural frequency that ensure the asymptotic stability of the cluster synchronization manifold are derived, showing that cluster synchronization is stable when the intracluster coupling is sufficiently stronger than the intercluster coupling.

Synchronization in complex network system with uncertainty

- Mathematics, Computer Science53rd IEEE Conference on Decision and Control
- 2014

The main contribution of this paper is to provide analytical characterization for the interplay of role played by the internal dynamics of the nonlinear systems, network topology, and uncertainty statistics for the network synchronization.

Stability Conditions for Cluster Synchronization in Networks of Kuramoto Oscillators

- Physics, Computer ScienceArXiv
- 2018

Quantitative conditions on the network weights, cluster configuration, and oscillators' natural frequency that ensure asymptotic stability of the cluster synchronization manifold are derived that ensure the ability to recover the desired cluster synchronization configuration following a perturbation of the oscillators states.

## References

SHOWING 1-10 OF 98 REFERENCES

Exploring synchronization in complex oscillator networks

- Physics, Computer Science2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
- 2012

A tutorial introduction to coupled oscillator networks, a review of the vast literature on theory and applications, and a collection of different synchronization notions, conditions, and analysis approaches are presented.

Synchronization and transient stability in power networks and non-uniform Kuramoto oscillators

- Mathematics, Computer ScienceProceedings of the 2010 American Control Conference
- 2010

A singular perturbation analysis shows the equivalence between the classic swing equations and a non-uniform Kuramoto model characterized by multiple time constants, non-homogeneous coupling, and non- uniform phase shifts.

From incoherence to synchronicity in the network Kuramoto model.

- Mathematics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

It is analytically explained the existence of an intermediate regime of behavior between incoherence and synchronization, where system wide periodic behaviors are exhibited and stable, unstable, and hyperbolic fixed points can be identified.

Synchronization of Kuramoto oscillators in scale-free networks

- Computer Science, Physics
- 2004

It is found that the resynchronization time of a perturbed node decays as a power law of its connectivity, providing a simple analytical explanation to this interesting behavior.

Synchronization in symmetric bipolar population networks.

- Mathematics, PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

This paper presents an analytical estimation for the minimum value of the coupling strength between oscillators that guarantees the achievement of a globally synchronized state and provides a better understanding of the effect of topological localization of natural frequencies on synchronization dynamics.

On the Critical Coupling for Kuramoto Oscillators

- Physics, MathematicsSIAM J. Appl. Dyn. Syst.
- 2011

It is proved that the multi-rate Kuramoto model is locally topologically conjugate to a first-order Kuramoto models with scaled natural frequencies, and necessary and sufficient conditions for almost global phase synchronization and local frequency synchronization are presented.

On the stability of the Kuramoto model of coupled nonlinear oscillators

- Physics, MathematicsProceedings of the 2004 American Control Conference
- 2004

We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for all-to-all networks of identical oscillators. Our work is applicable to…

Collective dynamics of ‘small-world’ networks

- Computer Science, MedicineNature
- 1998

Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.

Hierarchical Clustering of Dynamical Networks Using a Saddle-Point Analysis

- Mathematics, Computer ScienceIEEE Transactions on Automatic Control
- 2013

It is proven that cluster synchronization appears asymptotically independent of the initial conditions, and the clustering behavior of the dynamic network is shown to correspond to the solution of a static saddle-point problem, enabling a precise characterization of the clustered structure.